Propagation of Normal Axisymmetric Waves in Compliant Elastic Cylinders Filled with and Immersed in a Fluid

Komissarova, G. L.

doi:10.1023/b:inam.0000037304.96739.27

International Applied Mechanics

2004

DOI: 10.1023/b:inam.0000037304.96739.27

|View full text |Cite

Propagation of Normal Axisymmetric Waves in Compliant Elastic Cylinders Filled with and Immersed in a Fluid

G. L. Komissarova

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2005

2008

Publication Types

Select...

Article2

Relationship

Self Cite1

Independent1

Authors

Journals

Cited by 2 publications

(2 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A numerical analysis of the dispersion equations reveals spectral branches of traveling normal waves with different types of symmetry of cross-sectional displacements and different circumferential wave numbers. Some features of the spectrum due to variation in the angular measure are established Keywords: longitudinally anisotropic cylindrical waveguide, sector-shaped channel, traveling normal waves, dispersion spectrumThe varying properties of the dispersion spectra of harmonic normal strain waves in elastic cylindrical waveguides and the possibilities to control the structure of dispersion spectra by varying the geometry of the cross-section and the mechanical properties of the waveguide and using the effects of coupling of physicomechanical fields or filling hollow cylindrical waveguides with a fluid are issues partially generalized in [1-4] and remaining important for wave mechanics [5][6][7][8][9][10][11].The present paper discusses results describing the changes in the structure of the dispersion spectra of traveling normal waves in longitudinally anisotropic cylindrical waveguides of sector-shaped cross-section with a variable angular measure (Fig. 1).…”

mentioning

confidence: 99%

“…The varying properties of the dispersion spectra of harmonic normal strain waves in elastic cylindrical waveguides and the possibilities to control the structure of dispersion spectra by varying the geometry of the cross-section and the mechanical properties of the waveguide and using the effects of coupling of physicomechanical fields or filling hollow cylindrical waveguides with a fluid are issues partially generalized in [1][2][3][4] and remaining important for wave mechanics [5][6][7][8][9][10][11].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Dispersion Spectrum of an Anisotropic Waveguide with Sector-Shaped Cross Section and Fixed Boundary

2005

View full text Add to dashboard Cite

The dispersion equations are derived analytically for normal elastic waves in a longitudinally anisotropic cylindrical waveguide with circular cross-section and a sector-shaped channel of arbitrary angular measure. The boundary surfaces of the channel are covered with flexible, inextensible membranes. The cylindrical portion of the lateral surface is rigidly fixed. A numerical analysis of the dispersion equations reveals spectral branches of traveling normal waves with different types of symmetry of cross-sectional displacements and different circumferential wave numbers. Some features of the spectrum due to variation in the angular measure are established Keywords: longitudinally anisotropic cylindrical waveguide, sector-shaped channel, traveling normal waves, dispersion spectrumThe varying properties of the dispersion spectra of harmonic normal strain waves in elastic cylindrical waveguides and the possibilities to control the structure of dispersion spectra by varying the geometry of the cross-section and the mechanical properties of the waveguide and using the effects of coupling of physicomechanical fields or filling hollow cylindrical waveguides with a fluid are issues partially generalized in [1-4] and remaining important for wave mechanics [5][6][7][8][9][10][11].The present paper discusses results describing the changes in the structure of the dispersion spectra of traveling normal waves in longitudinally anisotropic cylindrical waveguides of sector-shaped cross-section with a variable angular measure (Fig. 1). The waveguide occupies the following domain described in dimensionless cylindrical coordinates: V = {r ∈ [0, R * ], θ ∈ [α, 2π -α], z ∈ (-∞, ∞)}. The cross-sectional boundary G = G 0 ∪ G + ∪ G -of the waveguide consists of the following sections G 0 = {r = R * , α ≤ θ ≤ 2π -α}, G + = {0 ≤ r ≤ R * , θ = α}, and G -= { 0 ≤ r ≤ R * , θ = -α}. The section G 0 is fixed, and the sector-shaped channel, G + and G -, is covered with perfectly elastic, inextensible membranes. These boundary conditions are expressed aswhere { }( , , ) u r z α α θ = are the dimensionless components of the vector intensity function r r u u r e i t kz = − − 0 ( , ) (~) θ ω for a harmonic normal wave, and { }( , , , , ) σ αβ θ θθ θ αβ = rr r rz z are dimensionless complex elastic-stress functions for normal waves. The dispersion equation for the normal waves in question is derived analytically. By integrating the stationary dynamic equations of an anisotropic hexagonal-system medium with OZ as a collinear symmetry axis, we obtain the dimensionless normalized components of the complex amplitude vector r u 0 of wave displacements: u r

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

Dispersion Spectrum of an Anisotropic Waveguide with Sector-Shaped Cross Section and Fixed Boundary

2005

View full text Add to dashboard Cite

show abstract

Localization of wave motions in a fluid-filled cylinder

Komissarova

2008

Int Appl Mech

Self Cite

View full text Add to dashboard Cite

The properties of harmonic surface waves in a fluid-filled cylinder made of a compliant material are studied. The wave motions are described by a complete system of dynamic equations of elasticity and the equation of motion of a perfect compressible fluid. An asymptotic analysis of the dispersion equation for large wave numbers and a qualitative analysis of the dispersion spectrum show that there are two surface waves in this waveguide system. The first normal wave forms a Stoneley wave on the inside surface with increase in the wave number. The second normal wave forms a Rayleigh wave on the outside surface. The phase velocities of all the other waves tend to the velocity of the shear wave in the cylinder material. The dispersion, kinematic, and energy characteristics of surface waves are analyzed. It is established how the wave localization processes differ in hard and compliant materials of the cylinder Keywords: fluid-filled elastic cylinder, dispersion equation, asymptotic analysis, wave number, first and second normal waves, Stoneley and Rayleigh waves, hard and compliant materialsIntroduction. Since Rezal', Gromeko, Kortevoi, and Zhukovski who studied wave motions in fluid-filled pipes, both hard and soft (compliant) materials of the pipe have been considered [11]. They derived approximate expressions for the phase velocity of the lowest normal wave. Study of the properties of normal waves in fluid-filled cylinders is stimulated by a number of applied problems. Of interest are normal waves of low and high orders.An analysis of accumulated data on the properties of normal waves in compound waveguides such as an elastic body with a fluid shows that it is expedient to systematize them by estimating the ratio between the speed of sound in the fluid and the velocity of shear waves in the material of the cylinder [16,17]. If the latter exceeds the former ( ) V C S > 0 , the phase velocities of all normal waves in the compound waveguide, except for the lowest one, tend from above to the speed of sound in the fluid [16]. We will call the associated material of the cylinder hard. If the velocity of shear waves is lower than the speed of sound in the fluid ( ) V C S < 0 , the material of the cylinder will be called soft or compliant. The density of the compliant material is slightly greater than or equal to the density of the fluid. The density of the hard material is much greater than the density of the fluid.Rayleigh and Stoneley were the first to study surface waves in an elastic body [18,21]. The classical Rayleigh wave exists near the free flat surface of an elastic half-space. The Stoneley wave can exist at the flat interface between two elastic media. This wave exists only at certain ratios between the stiffness characteristics of the contacting media [3]; and there are a limited number of pairs of materials with such characteristics. Stoneley waves always exist at the interface between liquid and elastic media [10,20].The Rayleigh and Stoneley waves are monochromatic and nondispersive (the phase velocity is ...

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Propagation of Normal Axisymmetric Waves in Compliant Elastic Cylinders Filled with and Immersed in a Fluid

Cited by 2 publications

References 17 publications

Dispersion Spectrum of an Anisotropic Waveguide with Sector-Shaped Cross Section and Fixed Boundary

Dispersion Spectrum of an Anisotropic Waveguide with Sector-Shaped Cross Section and Fixed Boundary

Localization of wave motions in a fluid-filled cylinder

Contact Info

Product

Resources

About